Question

simplify \\( \sqrt{288} \\) to the form \\( a\sqrt{b} \\).

Explanation:

Step1: Factor 288 into perfect square and other

Find the largest perfect square factor of 288. We know that \(144\times2 = 288\), and 144 is a perfect square (\(12^2 = 144\)). So, \(\sqrt{288}=\sqrt{144\times2}\).

Step2: Use square root property

Using the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0\) and \(b\geq0\)), we can split the square root: \(\sqrt{144\times2}=\sqrt{144}\times\sqrt{2}\).

Step3: Simplify \(\sqrt{144}\)

Since \(\sqrt{144} = 12\) (because \(12\times12 = 144\)), we substitute that in: \(12\times\sqrt{2}=12\sqrt{2}\).

Answer:

\(12\sqrt{2}\)